I can speak to having a generator in the bed of the truck but not on the back bumper. Our generator is a Yamaha 6300 inverter generator and weighs over 200 lbs. I drop that down into my truck bed at the beginning of the camping season and leave it there till we are finished for the season. For me it's too heavy to move in and out and I don't want to have to move the Companion hitch either. Mine is gas and I chose that fuel for a reason due to fuel availably and power deration which happens at altitude where we live here in CO. I have a remote start on the generator and often would leave my camper plugged into it once I arrived at my site. I could then start the generator from my remote and then wait for the EMS device to analyze the feeds before it made the final connection. Works great. This year I changed up our whole electrical system and added solar and have not used the generator once all year and likely will not. I still have it in the bed of the truck for backup but my Lithium batteries and solar are doing the trick for us. I was worried about the large amount of weight at the very back of my camper and any teetering that would take place. Many have concerns with lots of weight in the very back with bouncing and etc. Your solution is much less weight and may not present those concerns. We also carry our electric bikes on a bike rack on the GD provided hitch.

I used to run my old Honda generator in the back of my truck, and it would sometimes sputter and stall. After experimenting, I found that the exhaust gasses were recirculating to the intake and causing it to run poorly. I placed the generator on some wood blocks and that got it high enough to get fresh air to the intake and solved that problem.

I have two small Champion generators now, so I just place them on the ground when I need them. But I see nothing wrong with your plan. I currently run about 125 pounds of bikes and racks on my receiver hitch and it works great.

Jim